Statistical linear models in Procrustes shape space

Abstract : The configuration matrix of a set of labeled landmarks is one the most used shape representations. However, it is well-known that the configuration matrix is not invariant under translation, scaling and rotation. This problem is revisited in this work where a local tangent shape space characterization at a reference shape is obtained as the null space of the subspace spanned by the reference shape and the set of translation and rotation generators. This local linear description of the shape space allows us to compute mean and variance of shapes as well as apply classical mutivariate statistical techniques such as Principal Component Analysis. Our proposal is compared with previous approaches, such as the seminal work [1] and more recents works [2] and [3].
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Xavier Pennec and Sarang Joshi. 1st MICCAI Workshop on Mathematical Foundations of Computational Anatomy: Geometrical, Statistical and Registration Methods for Modeling Biological Shape Variability, Oct 2006, Copenhagen, Denmark. pp.102-111, 2006
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Matias Bossa, Salvador Olmos. Statistical linear models in Procrustes shape space. Xavier Pennec and Sarang Joshi. 1st MICCAI Workshop on Mathematical Foundations of Computational Anatomy: Geometrical, Statistical and Registration Methods for Modeling Biological Shape Variability, Oct 2006, Copenhagen, Denmark. pp.102-111, 2006. 〈inria-00635901〉

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